# Relative Time Question

1. Sep 28, 2010

### ConstantineWW

I am a total physics idiot, but I do enjoy writing, I do enjoy science fiction, and I'd like to run this concept by people who know they're talking about.

So - time is relative, yes? If I count five seconds where I am, it is possible that ten seconds are passing in that same span of time for someone elsewhere, yes?

So, I'm in a room where time moves five times faster on one side than on the other. I throw a baseball at 10 mph from the fast side to the slow side - does anything actually happen to the velocity of the ball? Does it appear to me to slow down, even though it velocity never changes; or does it hit the wall of the slow side at 50 mph? I suspect I know the answer to this (it would just look like it got slower to me without actually changing velocity, right?) so I'll ask one more to my point.

Let's assume there's a box; time moves five times faster inside this box than it does outside. If I were to put my hand inside the box, what would happen? Particularly consider my blood -it's now flowing into an area where time moves faster, and flowing out of that arm into an area where time moves slower. This might be more of a biology question, insofar as it's a respectable question at all, but would I suffer any deleterious effects by putting my arm in such a box?

2. Sep 28, 2010

### mathman

Clocks go relatively fast or slow due to relativity effects, such as motion or acceleration. If the clocks are stationary with respect to each other they will keep the same time (not counting an extremely small effect from general relativity).

Your examples with the baseball and the box just can't happen, since there is no relative motion.

3. Sep 28, 2010

### ConstantineWW

Correct me if I'm wrong - a very plausible scenario - but can't clocks go relatively fast or slow from by being in different levels of gravity, too? As in, if a stationary clock were a mile away from a black hole, it would appear to be slower than a stationary clock a thousand miles away?

4. Sep 28, 2010

### JesseM

Even the notion of the "same span of time" is relative, because simultaneity is relative for events which occur at different locations in space. Suppose I am moving past you at 0.6c, and at the moment we pass by each other both of us set our clocks to zero. Then in your rest frame the event of your clock reaching 5 seconds is simultaneous with the event of my clock reaching 4 seconds, so according to your frame's definition of simultaneity less time has passed for me than for you in this "span of time". But in my rest frame the event of your clock reaching 5 seconds is simultaneous with the event of my clock reaching 6.25 seconds, so according to my frame's definition of simultaneity more time has passed for me than for you in this "span of time".
In the absence of gravity ('special relativity'), time dilation is only based on speed, not location, at least if we are using an inertial frame as is usually done in special relativity. In the theory of "general relativity" which includes gravitation, there's an infinite variety of equally valid frames (a 'frame' is a spacetime coordinate system which is used to assign position and time coordinates to every point in space and time) to choose from, with different simultaneity conventions. In the spacetime around a spherical planet, the most commonly-used coordinate system would be Schwarzschild coordinates, and in these coordinates a clock closer to the center of the planet would be ticking slower than a clock farther from the center.
There's ambiguity in your question because when you use words like "appear" it's not clear if you're talking about the coordinate speed in some frame like Schwarzschild coordinates, or if you're talking about actual visual appearances, how far away it looks to you at different times according to your own clock. The first depends on your choice of coordinate system while the second is coordinate-independent.

5. Sep 28, 2010

### Staff: Mentor

In SR this cannot happen, in GR it could in principle (but might require exotic matter). The tidal forces would probably tear your hand apart.

6. Sep 28, 2010

### DrGreg

Something like this could happen, even in the absence of gravity, if you were undergoing extremely high acceleration. But to get that amount of time dilation over such a short distance would require such a huge acceleration that any human body would be crushed to death.